R’ Yochanan said in the name of Rebi Shimon ben Yehotzedek: There are eighteen days that one recites a full Hallel : Eight days of the Festival of Sukkos, eight days of Chanukah, the first day of Pesach, Yom Tov of Atzeret (Shavuous), and in the Diaspora, twenty days: nine days of the Festival Of Sukkos, two yom tov days of Pesach and two days of Shavuous. – Talmud Arachin

BACKGROUND
1. Our prophets established the recitation of the Hallel prayer, which literally means praises, to be recited during the morning prayers of Festivals, and times of National redemption. Hallel’s six Pslams (113-118) area recited together at these joyous times to show thanksgiving, praise, and faith in G-d.
2. Hallel was recited by Moshe and Israel, by Joshua, and Debrah and Barak, when they were saved from their enemies. These Pslams were incorporated into the Book of Pslams by King David.
3. Hallel reflects five basic elements of Jewish faith: The Exodus from Egypt, the Splitting of the Red Sea, Giving of the Torah at Sinai, the Resurrection of The Dead, and the Coming of the Moshiach.
4. Hallel is not recited on Rosh Hashanah, Yom Kippur or Purim. On Rosh Chodesh and the Chol Hamoed days of Pesach, we omit the first two halves of Psalms 115, and 116.
5. A basic commentary on Hallels is provided in the Artscroll Siddur.
BASIC LAWS OF THE RECITATION OF HALLEL ON SUKKOS
1. We finish Hallel every day of Sukkos.
2. It is a mitzvah to recite the Hallel while standing, without leaning on anything. If for any reason a person cannot stand, they are still permitted to say Hallel.
3. Refrain from speaking during the entire Hallel, whether a full or short Hallel.
4. If one knows the words of Hallel by heart, they may recite it without a siddur.
5. Do not make pause between the recitation of the Hallel blessing and the start of the Hallel Psalms. If you do make an interruption, go back and say the blessing again.
6. If you are interrupted or pause between paragraphs, finish Hallel from where you left off.
7. If you started Hallel without a lulav and esrog, and someone hands you them: Stop between paragraphs and recite the blessing for the lulav and esrog, (which appears in the siddur before Hallel), and then continue Hallel where you left off.
8. If you prayed Hallel, and later realized you recited the short Hallel on a day that we recite a full Hallel, recite Hallel again.
9. If you walk into synagogue and they are reciting Hallel, recite Hallel with the congregation and then afterwards say your morning prayers.